Calculating the gains
CNT-APG002-EN 11
®
Calculating the gains
Table1 shows recommended initial values for the proportional and inte-
gral gains for several applications. Most applications do not require a
derivative contribution, so the derivative gain is not shown. We recom-
mend using a ratio of 4:1 between the proportional and integral gains, so
the proportional gain should be four times as large as the integral gain.
You may need to modify the values shown in Table1 when tuning a PID
loop, but try to maintain the 4:1 ratio.
You can also calculate proportional and integral gains using the following
calculations:
The proportional gain is scaled by a factor of 0.80, so it contributes 80% of
the final output. The integral gain contributes 20% of the final output.

Example

In a duct static pressure system, an actuator can move the inlet guide
vanes of an air handler from 0–100%, so the output range is 100. We want
a throttling range of 2.0 in. wc (so a change in pressure of 2.0 in. wc or
more will drive the output from 0–100% or vice versa). Th e calculations
look like this:
So based on the desired throttling range of 2.0 in. wc, the initial propor-
tional gain is 40 and the integral gain is 10.
Table 1: Starting gain values for applications
Application Output Throttling range
Proportional
gain
Integral
gain
Discharge-air cooling Valve position 0–100% 20.0°F (11.1°C) 4.0 (8.0) 1.0 (2.0)
Discharge-air heating Valve position 0–100% 40.0°F (22.2°C) 2.0 (4.0) 0.5 (1.0)
Space temperature Discharge setpoint
50–100°F (10–37.8°C)
2.0°F (1.1°C) 20.0 (20.0) 5.0 (5.0)
Duct static pressure Inlet guide vane or variable-frequency
drive (VFD) position 0–100%
2.0 in. wc (0.5 kPa) 40.0 (160) 10.0 (40.0)
Building static
pressure
Inlet guide vane or variable-frequency
drive (VFD) position 0–100%
20.0 in. wc (5.0 kPa) 4.0 (8.0) 1.0 (2.0)
Discharge-air cooling Electric/pneumati c
5.0–15.0 psi (34–103 kPa)
20.0°F (11.1°C) 0.4 (4.0) 0.1 (1.0)
Proportional gain 0.80 output range×
throttling range
--------------------------------------------------------=
Integral gain 0.20 outpu t range×
throttling range
--------------------------------------------------------=
Proportional gain 0.80 output range×
throttling range
------------------------------------------------------0.80 100×
2.0in. wc
----------------------------40===
Integral gain 0.20 output range×
throttling range
------------------------------------------------------0.20 100×
2.0in. wc
----------------------------10===